1. Field of the Invention
This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to the field of seismic data processing. Specifically, the invention is a method for imaging the earth through seismic migration.
2. Description of the Related Art
In the oil and gas industry, geophysical prospecting is commonly used to aid in the search for and evaluation of subterranean formations. Geophysical prospecting techniques yield knowledge of the subsurface structure of the earth, which is useful for finding and extracting valuable mineral resources, particularly hydrocarbon deposits such as oil and natural gas. A well-known technique of geophysical prospecting is a seismic survey. In a land-based seismic survey, a seismic signal is generated on or near the earth's surface and then travels downward into the subsurface of the earth. In a marine seismic survey, the seismic signal may also travel downward through a body of water overlying the subsurface of the earth. Seismic energy sources are used to generate the seismic signal which, after propagating into the earth, is at least partially reflected by subsurface seismic reflectors. Such seismic reflectors typically are interfaces between subterranean formations having different elastic properties, specifically sound wave velocity and rock density, which lead to differences in acoustic impedance at the interfaces. The reflected seismic energy is detected by seismic sensors at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes and recorded.
The appropriate seismic sources for generating the seismic signal in land seismic surveys may include explosives or vibrators. Marine seismic surveys typically employ a submerged seismic source towed by a ship and periodically activated to generate an acoustic wavefield. The seismic source generating the wavefield may be of several types, including a small explosive charge, an electric spark or arc, a marine vibrator, and, typically, a gun. The seismic source gun may be a water gun, a vapor gun, and, most typically, an air gun. Typically, a marine seismic source consists not of a single source element, but of a spatially-distributed array of source elements. This arrangement is particularly true for air guns, currently the most common form of marine seismic source.
The appropriate types of seismic sensors typically include particle velocity sensors, particularly in land surveys, and water pressure sensors, particularly in marine surveys. Sometimes particle displacement sensors, particle acceleration sensors, or pressure gradient sensors are used in place of or in addition to particle velocity sensors. Particle velocity sensors and water pressure sensors are commonly known in the art as geophones and hydrophones, respectively. Seismic sensors may be deployed by themselves, but are more commonly deployed in sensor arrays. Additionally, pressure sensors and particle velocity sensors may be deployed together in a marine survey, collocated in pairs or pairs of arrays.
The resulting seismic data obtained in performing the survey is processed to yield information relating to the geologic structure and properties of the subterranean formations in the area being surveyed. The processed seismic data is processed for display and analysis of potential hydrocarbon content of these subterranean formations. The goal of seismic data processing is to extract from the seismic data as much information as possible regarding the subterranean formations in order to adequately image the geologic subsurface.
In order to identify locations in the Earth's subsurface where there is a probability for finding petroleum accumulations, large sums of money are expended in gathering, processing, and interpreting seismic data. A crucial step in processing seismic data is seismic migration. Seismic migration is the process of constructing the reflector surfaces defining the subterranean earth layers of interest from the recorded seismic data. The processing procedure of seismic migration provides an image of the earth in depth or time.
The image of the structure of the Earth's subsurface is produced in order to enable an interpreter to select locations with the greatest probability of having petroleum accumulations. To verify the presence of petroleum, a well must be drilled. Drilling wells to determine whether petroleum deposits are present or not, is an extremely expensive and time-consuming undertaking. For that reason, there is a continuing need to improve the processing and display of the seismic data, so as to produce an image of the structure of the Earth's subsurface that will improve the ability of an interpreter, whether the interpretation is made by a computer or a human, to assess the probability that an accumulation of petroleum exists at a particular location in the Earth's subsurface.
Migration is intended to account for both positioning and amplitude effects associated with the transmission and reflection of seismic energy from seismic sources to seismic receivers. Since transmission and reflection occurs in three rather than two dimensions, migration is better performed in three rather than two dimensions. However, three-dimensional (3-D) migration is computationally more complicated than two-dimensional (2-D) migration, because azimuth effects are involved. Thus, 3-D migration is more expensive than 2-D migration.
In practice, this complication with azimuths presents many more challenges for inhomogeneous (vertically or laterally varying velocity) media than for homogeneous (constant velocity) media. Most 3-D migration algorithms for inhomogeneous media comprise implementation of complicated one-pass 3-D migration operators. Great efforts have been dedicated to resolving the azimuth effects inherent in all 3-D migration operators and computations.
Consequently, one approach in the development of 3-D seismic imaging has been an attempt to reduce 3-D migration back to the less expensive 2-D migration. Because of the azimuth effects involved in 3-D operators and calculations, 3-D migration can not generally be realized exactly by implementation of 2-D migration algorithms. So, only limited success has been achieved and only exactly in the constant velocity case, using two-step (or two-pass) migration methods. Two examples of two-step migration techniques are described here.
Gibson B., Lamer, K., and Levin, S., in their 1983 article, “Efficient 3-D migration in two-steps”, Geophysical Prospecting, Vol. 31, p. 1-33, describe a two-step 3-D post-stack time migration, utilizing cascading 2-D time migrations as a substitute for 3-D post-stack time migration. This two-step approach first migrates all time sections in one direction with a 2-D algorithm and then sorts the resulting data into time sections in the orthogonal direction and migrates all these sections with a 2-D algorithm. Gibson et al. (1983) show that their method provides increased efficiency when applied to Kirchhoff summation and finite difference techniques, but is found to be less efficient than conventional one-pass 3-D migration in the frequency-wavenumber domain. The method is exact for homogeneous media, but not for inhomogeneous media. For vertically inhomogeneous media, the correct migration velocity is unavailable for the first 2-D migration step, so migrated positions are inaccurate. For laterally inhomogeneous media, Gibson et al. (1983) cannot provide the required depth migration version.
Devaux, V., G. H. F. Gardner, and T. Rampersad, in their 1996 article, “3-D pre-stack depth migration by Kirchhoff operator splitting”, 66th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, p. 455-458, describe two-step 3-D pre-stack depth migration, utilizing two alternating 2-D migrations as a substitute for 3-D pre-stack depth migration. The first step is a 2-D time migration in the cross-line direction. The second step is an iterative 2-D depth migration in the in-line direction, with the velocity model being updated between iterations. Devaux et al. (1996) state that their 2-D method is equivalent to full 3-D pre-stack depth migration for constant velocity media, but only an approximation for variable velocity media.
Therefore, migrating 3-D seismic data in a general inhomogeneous velocity media is conventionally done with either a one-pass implementation of 3-D migration operators or with a two-pass implementation of 3-D migration by 2-D migration operators that is only an approximation. A one-pass 2-D migration operator would be computationally much less expensive than the one-pass implementation of 3-D migration operators, but much more accurate than the approximate two-pass implementation of 3-D migration.
Pan, N., et al., (including the present inventor) in their 1992 article, “Efficient 3-D filtering using projected 2-D true-dip sections”, 62nd Annual International Meeting, SEG, Expanded Abstract, p. 1042-1045, describe a transform method for 3-D post-stack time migration which can accomplish exact 3-D time migration by using any accurate 2-D migration algorithm. The method of Pan et al. (1992) is a one-pass implementation of a 2-D migration operator as a substitute for 3-D seismic migration, at least for the post-stack time migration case.
However, in areas with structural complexity, seismic migration should be performed with pre-stack data and in the depth domain, rather than post-stack in the time domain, in order to obtain more accurate stacked images. This, too, is computationally more expensive in general. Pan et al. (1992) does not discuss how to handle pre-stack data or depth migration.
Thus, a need exists for a transformation method to reduce a one-pass 3-D migration operator to a one-pass 2-D migration operator for general inhomogeneous media, which applies to pre- or post-stack data, time or depth migration.